Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class FunkyNumbers {
    public static void main(String[] args) {
        Scanner  sc=new Scanner(System.in);
        int n=sc.nextInt();
        n*=2;

        for(int i=1;i<=Math.sqrt(n);i++){
            int tmp=i*(i+1);
            int key=n-tmp;
            int l=i,r=(int)Math.sqrt(n);
            while(l<=r){
                int mid=l+(r-l)/2;
                if(mid*(mid+1)<key){
                    l=mid+1;
                }else if(mid*(mid+1)>key){
                    r=mid-1;
                }else{
                    System.out.println("YES");
                    return;
                }
            }
            
        }

        System.out.println("NO");

        sc.close();
    }
}